There is little to these claims. While the postal service is struggling, it's not because of Amazon. In fact, package delivery is one of the few lines of business that's growing.
The postal service has lost money for 11 straight years, mostly because of pension and health care costs. In 2017, the service
lost $800 million on $69.7 billion operating revenue. Under a 2006 law, it must pre-fund 75 years' worth of retiree health benefits. Neither the government nor private companies are required to do that. (It has defaulted on those payments periodically, with the last one made in 2015).
A widely cited Citigroup analysis from last year holds that the "true" cost of shipping packages for the Postal Service is about 50 percent higher than what it currently charges. "It is as if every Amazon box comes with a dollar or two stapled to the packing slip -- a gift card from Uncle Sam," read the ensuing editorials.
But Citi arrived at that figure by re-allocating the Post Office's benefits costs -- not the costs specific to package delivery.
The 2006 law also mandated that each line of business within the postal service cover its attributable costs. In other words, for the postal service to lose money on package delivery would be against the law.